You can go ahead and put your new address on your tax return. If you are due a tax refund, but having that refund deposited into your current bank account, you will be fine. Even if you were going to get a check mailed to you, I doubt that check would come in that time frame. Otherwise, you can put your current address on the tax return and just have your mail forwarded. You will want to do this in case your return has issues and the IRS mails you a notification.